Example 1.  Find the Padé approximation for .  

Solution 1.

First, set up the equation   .

Second, solve the equation   .

Compare our work with Mathematica's Pade subroutine.

Plot graphs of the function and its Pade approximation over the interval  [-1,1].  

Find the error  over the interval  [-1,1].  

Compare with the error in a degree Maclaurin polynomial over the interval  .  

Find the error  over the interval  [-1,1].  

Compare with the error in a degree Maclaurin polynomial over the interval  .  

Find the error  over the interval  [-1,1].  

(c) John H. Mathews 2004